Question: $ 100^{-\frac{3}{2}}$
$= \left(\dfrac{1}{100}\right)^{\frac{3}{2}}$ $= \left(\left(\dfrac{1}{100}\right)^{\frac{1}{2}}\right)^{3}$ To simplify $\left(\dfrac{1}{100}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=\dfrac{1}{100}$ To simplify $\left(\dfrac{1}{100}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({\dfrac{1}{10}}\right)^{2}=\dfrac{1}{100}$ so $ \left(\dfrac{1}{100}\right)^{\frac{1}{2}}=\dfrac{1}{10}$ So $\left(\dfrac{1}{100}\right)^{\frac{3}{2}}=\left(\left(\dfrac{1}{100}\right)^{\frac{1}{2}}\right)^{3}=\left(\dfrac{1}{10}\right)^{3}$ $= \left(\dfrac{1}{10}\right)\cdot\left(\dfrac{1}{10}\right)\cdot \left(\dfrac{1}{10}\right)$ $= \dfrac{1}{100}\cdot\left(\dfrac{1}{10}\right)$ $= \dfrac{1}{1000}$